Skip to main content

Reaching a goal with directional uncertainty

  • Conference paper
  • First Online:
Algorithms and Computation (ISAAC 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 762))

Included in the following conference series:

  • 159 Accesses

Abstract

We study two problems related to planar motion planning for robots with imperfect control, where, if the robot starts a linear movement in a certain commanded direction, we only know that its actual movement will be confined in a cone of angle α centered around the specified direction.

This research was supported by the Netherlands' Organization for Scientific Research (NWO) and partially by ESPRIT Basic Research Actions No. 6546 (project PROMotion) and No. 7141 (project ALCOM II: Algorithms and Complexity). Part of the research was done during the Second Utrecht Workshop on Computational Geometry and its Application, supported by NWO. L.G. acknowledges support by NSF grant CCR-9215219, by a grant from the Stanford SIMA Consortium, and by grants from the Digital Equipment, Mitsubishi, and Toshiba Corporations. D.H. was supported by a Rothschild Postdoctoral Fellowship, by a grant from the Stanford Integrated Manufacturing Association (SIMA), and by NSF/ARPA Research Grant IRI-9306544. Work on this paper by M.S. has been supported by National Science Foundation Grant CCR-91-22103, and by grants from the U.S.-Israeli Binational Science Foundation, the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. B. Bhattacharya, D. G. Kirkpatrick, and G. T. Toussaint. Determining sector visibility of a polygon. In Proc. 5th Annu. ACM Sympos. Comput. Geom., pages 247–254, 1989.

    Google Scholar 

  2. A. J. Briggs. An efficient algorithm for one-step planar compliant motion planning with uncertainty. In Proc. 5th Annu. ACM Sympos. Comput. Geom., pages 187–196, 1989.

    Google Scholar 

  3. B. R. Donald. The complexity of planar compliant motion planning under uncertainty. Algorithmica, 5:353–382, 1990.

    Article  Google Scholar 

  4. H. Edelsbrunner, L. J. Guibas, and M. Sharir. The complexity and construction of many faces in arrangements of lines and of segments. Discrete Comput. Geom., 5:161–196, 1990.

    Google Scholar 

  5. M. Erdmann. On motion planning with uncertainty. Technical Report 810, AI Laboratory, MIT, 1984.

    Google Scholar 

  6. J. Friedman, J. Hershberger, and J. Snoeyink. Compliant motion in a simple polygon. In Proc. 5th Annu. ACM Sympos. Comput. Geom., pages 175–186, 1989.

    Google Scholar 

  7. J. Friedman, J. Hershberger, and J. Snoeyink. Input-sensitive compliant motion in the plane. In Proc. 2nd Scand. Workshop Algorithm Theory, volume 447 of Lecture Notes in Computer Science, pages 225–237. Springer-Verlag, 1990.

    Google Scholar 

  8. P. Heckbert and J. Winget. Finite-element methods for global illumination. To appear.

    Google Scholar 

  9. K. Kedem, R. Livne, J. Pach, and M. Sharir. On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles. Discrete Comput. Geom., 1:59–71, 1986.

    Google Scholar 

  10. J.-C. Latombe. Robot Motion Planning. Kluwer Academic Publishers, Boston, 1991.

    Google Scholar 

  11. A. Lazanas and J.-C. Latombe. Landmark-based robot navigation. Submitted to Algorithmica.

    Google Scholar 

  12. T. Lozano-Pérez, M. T. Mason, and R. H. Taylor. Automatic synthesis of finemotion strategies for robots. Internat. J. Robotics Research, 3:3–24, 1984.

    Google Scholar 

  13. J. Matousek, N. Miller, J. Pach, M. Sharir, S. Sifrony, and E. Welzl. Fat triangles determine linearly many holes. In Proc. 32nd Annu. IEEE Sympos. Found. Comput. Sci., pages 49–58, 1991.

    Google Scholar 

  14. M. van Kreveld. On fat partitioning, fat covering, and the union size of polygons. In Proc. 3rd Workshop Algorithms Data Struct., Lecture Notes in Computer Science, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

K. W. Ng P. Raghavan N. V. Balasubramanian F. Y. L. Chin

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

de Berg, M. et al. (1993). Reaching a goal with directional uncertainty. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_229

Download citation

  • DOI: https://doi.org/10.1007/3-540-57568-5_229

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57568-9

  • Online ISBN: 978-3-540-48233-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics